A board was 24 3/8 inches long. A worker cut it intopieces that were 4 7/8 inches long. The worker cut theboard into how many pieces?
24 * 8 + 3 = 195 so 195/8
4*8 + 7 = 39 so 39/8
195/8 / 39/8 = 195/39 = 5
remarkably lucky
To find out how many pieces the worker cut the board into, we need to divide the length of the board by the length of each piece.
Length of the board = 24 3/8 inches
Length of each piece = 4 7/8 inches
To make it easier to divide, we can convert the mixed numbers to improper fractions:
Length of the board = 24 3/8 inches = (8 * 24 + 3) / 8 = 195/8 inches
Length of each piece = 4 7/8 inches = (8 * 4 + 7) / 8 = 39/8 inches
Now, let's divide the length of the board by the length of each piece:
Number of pieces = Length of the board / Length of each piece
Number of pieces = (195/8) / (39/8)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
Number of pieces = (195/8) * (8/39)
Simplifying the fractions:
Number of pieces = 195/39
The numerator represents the number of pieces the worker cut the board into:
Number of pieces = 195/39 = 5
Therefore, the worker cut the board into 5 pieces.
To find the number of pieces the worker cut the board into, we need to divide the length of the board by the length of each piece.
To do this, we'll convert the mixed numbers into improper fractions. "24 3/8" can be written as 24 + 3/8 = 192/8 + 3/8 = 195/8.
Now we divide the length of the board (195/8) by the length of each piece (4 7/8 or 39/8).
195/8 ÷ 39/8 = 195/8 × 8/39 (dividing by a fraction is the same as multiplying by its reciprocal)
Now, we multiply the numerators and denominators:
(195 × 8) / (8 × 39)
The denominator cancels out, so we are left with:
(195 × 1) / 39 = 195 / 39 = 5
Therefore, the worker cut the board into 5 pieces.